As is known, in the technical field of photon detection, the need is felt to have devices that enable detection of electromagnetic radiation with a high sensitivity, and hence that enable detection of even a limited number, of photons associated with the electromagnetic radiation itself.
For this purpose, the so-called “geiger-mode avalanche photodiodes” (GM-APDs) are known, which theoretically enable detection of individual photons.
A geiger-mode avalanche photodiode, also known as single-photon avalanche diode (SPAD), is formed by an avalanche photodiode (APD), and hence comprises a junction made of semiconductor material, which has a breakdown voltage VB and is biased, in use, with a reverse-biasing voltage VA higher in absolute value than the breakdown voltage VB of the junction (which, as is known, depends upon the semiconductor material and upon the level of doping of the least doped region of the junction itself), typically higher than 10-20%. In this way, the junction has a particularly extensive depleted region, present in which is a non-negligible electrical field. Hence, the generation of a single electron-hole pair, caused by absorption within the depleted region of a photon incident on the SPAD within the depleted region, may be sufficient to trigger an ionization process. The ionization process in turn causes an avalanche multiplication of the carriers, with gains in the region of 106, and consequent generation in short times (hundreds of picoseconds) of the so-called avalanche current, or more precisely of a pulse of the avalanche current.
The avalanche current may be appropriately collected, typically by means of external circuitry coupled to the junction, for example by appropriate anode and cathode contacts, and represents an output signal of the SPAD, also referred to as “output current”. In practice, in principle, for each photon absorbed, a pulse of the output current of the SPAD is generated.
It is noted that, strictly speaking, present across the junction is an effective voltage Ve, which coincides with the reverse-biasing voltage VA only in the absence of photons. In fact, in the presence of photons, and hence of current generated within the SPAD, the effective voltage Ve across the junction is less, in absolute value, than the reverse-biasing voltage VA. However, in the present document it is assumed, except where otherwise explicitly stated, that the effective voltage Ve across the junction coincides with the reverse-biasing voltage VA.
It is likewise noted that, upon generation of the output current, or rather of corresponding pulses of the output current, there may concur not only both of the carriers of each electron-hole pair that has been generated following absorption of a photon within the depleted region, but also, given the reverse biasing of the junction, the minority carriers of the electron-hole pairs that have been generated following absorption of a photon outside the depleted region, hence in a quasi-neutral region, i.e., with a substantially zero electrical field. For example, assuming a junction of a PN type with the P region set, with respect to the direction of propagation of the photons, upstream of the N region, both the electrons of the electron-hole pairs generated in the non-depleted portion of the P region of the junction (also known as “dead layer”) and the holes of the electron-hole pairs generated in the non-depleted portion of the N region of the junction (generally known as “epilayer”) may contribute to the output current.
In particular, the aforementioned minority carriers may cause generation of corresponding output current pulses in the case where they manage to diffuse as far as the depleted region before recombining.
However, even though they may also contribute to photon detection, the minority carriers of the electron-hole pairs that have been generated outside the depleted region typically require, in order to be able to reach the depleted region, diffusion times ranging (according to the generation point and the level of doping) between hundreds of picoseconds and tens of nanoseconds; therefore, they may hence be collected at the anode and cathode terminals with considerable delays. In this way, a deterioration of the performance of the SPADs may occur, in terms of rapidity in generation of an output current pulse following absorption of a photon, i.e., in terms of the so-called response time (timing) of the SPAD. In particular, the generation, in the output current, of so-called “diffusion tails” may occur.
That the reverse-biasing voltage VA is appreciably higher than the breakdown voltage VB causes the avalanche-ionization process, once triggered, to be self-sustaining. Consequently, once triggered, the SPAD is no longer able to detect photons, with the result that, in the absence of appropriate remedies, the SPADs described manage to detect arrival of a first photon, but not arrival of subsequent photons.
In order to be able also to detect these subsequent photons, it is necessary to quench the avalanche current generated within the SPAD, stopping the avalanche-ionization process, and in particular lowering, for a period of time known as “hold-off time”, the effective voltage Ve across the junction, so as to inhibit the ionization process and quench the avalanche current, as described hereinafter. Next, the initial conditions of biasing of the junction are restored, in such a way that the SPAD is again able to detect photons. In order to reduce the effective voltage Ve across the junction after absorption of a photon, SPADs may adopt so-called “quenching circuits”, either of an active or passive type. In particular, in the case of quenching circuits of a passive type, it is common to use quenching resistors, as described for example in United States Patent Applications Publication Nos.: US2010/0271108 and US2010/0148040, which are incorporated by reference.
As is known, the gain and probability of detecting a photon, i.e., the sensitivity of the SPAD, are directly proportional to the value of the reverse-biasing voltage VA applied to the SPAD. In fact, the more the reverse-biasing voltage VA exceeds, in absolute value, the breakdown voltage VB, the higher the probability of occurrence of an avalanche generation of charge carriers, given that it entails a widening of the depleted region and of the electrical field present therein.
However, high reverse biasing voltages VA are such that, even in the absence of incident photons (a dark condition), a single charge carrier, generated, for example, by transfer of thermal energy, may be sufficient to trigger the avalanche-ionization process, generating a so-called “dark current”, which may adversely interfere with normal use of the SPAD.
In particular, the generation of dark current may occur not only in the case where the aforementioned thermally generated carrier is generated within the depleted region, but also in the case where this thermally generated carrier is generated outside the depleted region and manages in any case to diffuse until it reaches the depleted region before recombining. In particular, given the reverse biasing of the junction of the SPAD, in addition to all the carriers generated thermally in the depleted region of the junction, also the minority carriers generated thermally outside the depleted region may contribute to the dark current, these latter minority carriers only in the aforesaid case where they manage to diffuse as far as the depleted region.
In practice, each of the aforementioned thermally generated minority carriers may generate a corresponding output current pulse, to which there does not correspond an effective detection of a photon. Under dark conditions, these output current pulses have a Poisson statistic, and the corresponding statistical mean value is known as “dark count rate” or “dark-noise rate”.
From a quantitative standpoint, the performance of a generic SPAD is quantified through the so-called quantum-detection efficiency (QDE), which is defined as the ratio between a first number of photons detected equal to the difference between the mean number of photons detected per unit time and the mean dark noise rate in said unit time, and a second number equal to the mean number of photons that effectively impinge on the SPAD in said unit time.
In greater detail, the quantum-detection efficiency QDE is equal to the product of a photon-absorption efficiency n and of an avalanche-triggering probability, the latter being defined as the probability of an electron-hole pair generated in the depletion region effectively triggering a self-sustaining avalanche-ionization process; in particular, this probability is not equal to unity, because there is a non-negligible probability of the carriers of the pair losing energy on account of lattice scattering, thus recombining in such a way that the avalanche-ionization process aborts.
As regards the photon-absorption efficiency η, to a first approximation (neglecting the contributions of the aforementioned minority carriers) it is given byη=(1−R)·e−αD·(1−e−αW)  (1)where: α is a coefficient of absorption of the photons by the semiconductor that forms the generic SPAD, and is inversely proportional to the wavelength of the photons; R is a power-reflection coefficient of an air-semiconductor interface or else an air-dielectric interface in the case where the photons, before impinging on the junction, impinge on one or more anti-reflection dielectric layers; W is the thickness of the depleted region; and D is the thickness of the non-depleted portion of the region of the junction that is located upstream with respect to the direction of propagation of the photons (in practice, the dead layer, i.e., the portion of semiconductor that the photons traverse before reaching the depleted region).
In order to improve the performance of SPADs, and in particular in order to optimize the signal-to-noise ratio, i.e., the ratio between an effective output current, which derives just from the absorption of photons, and the dark current, it is hence expedient to limit as much as possible the lattice defectiveness of the SPADs themselves. In fact, the main contribution to the dark count rate is given by the so-called phenomenon of Shockley-Read-Hall (SRH) generation through the so-called generation-recombination (G-R) centers, which are located within the forbidden band of the semiconductor material that forms the junction of the SPAD and are caused by lattice imperfections. By reducing the dark count rate, the duration of the so-called quiescence interval, i.e., the mean time interval that elapses between two successive output current pulses (in conditions of dark), increases. Given that, during the quiescence interval, it is possible to detect correctly arrival of the photons, the lower the dark count rate, the higher the probability of absorbing photons and of triggering the avalanche-ionization process, thus improving the overall performance of the SPADs in terms of signal-to-noise ratio. In this connection, given the same dark count rate, the signal-to-noise ratio may, be improved by increasing the quantum-detection efficiency QDE.
Traditionally, the junctions of SPADs of a known type are formed by means of direct ion-implantation processes, which entail the inevitable introduction of lattice imperfections, notwithstanding the execution of subsequent thermal treatments for the annealing of the defects and deactivation of the impurities.
In addition, principally on account of the aforementioned thermal treatments, the SPADs have respective junctions such that the corresponding dead layers have non-negligible thicknesses (up to a few hundreds of nanometers), with consequent decrease in the quantum-detection efficiency QDE, and hence decrease in the signal-to-noise ratio, in particular as regards highly energetic photons (for example, photons in the so-called “blue-near ultraviolet”). Again, the presence of dead layers with non-negligible thicknesses entails non-negligible dark currents, as well as possible deterioration in the performance in terms of response times, on account of the generation of diffusion tails.
Similar considerations may be made for the so-called SPAD arrays, and in particular for the so-called “silicon photomultipliers” (SiPMs), used to improve the performance that may be obtained with individual SPADs.
In detail, an SiPM is a particular SPAD array, formed by an array of SPADs grown on one and the same substrate and provided with respective quenching resistors (for example, of a vertical type) integrated in the SPADs, these quenching resistors being uncoupled and independent of one another. In addition, the anode and cathode contacts of each SPAD are configured so that they may be coupled to a single voltage generator. Consequently, the SPADs of the SiPM may be biased at one and the same reverse-biasing′ voltage VA; in addition, the avalanche currents generated inside them are multiplexed together so as to generate an output signal of the SiPM equal to the summation of the output signals of the SPADs.
In practice, the SiPM is a device with a wide area and high gain, capable of supplying, on average, an electrical output signal (current) proportional to the number of photons that impinge on the SiPM; however, SiPMs may present the same drawbacks as do the SPADs that compose them.